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Moments, Arms, & Moment Arms

In a perspective article on scapular stabilization, the concepts of moments and moment arms came up. My fuzziest understanding is that they are related to rotation around a joint. And angles. And math. Usually, I ignore such words and cleave to the bigger picture. But scapulae are enticing black boxes to me and in the case of this article, moments and their arms seemed crucial to an understanding of the author’s theory of departure. This was the sentence that tossed me over the cliff: “Therefore, equal muscle forces are not mandatory – and could be clinically undesirable – because the muscles have different moment arms and thus different mechanical advantages for causing angular rotation in the joint.” I knew I needed help.

Historically, when I’ve tried to educate myself about biomechanical stuff (moments, arms, angles, etc.), my eyes glaze over and I hear this sound. Its hard to find someone writing about these biomechanical concepts in language that I can apply to my own understanding of yoga postures. So I reached out to my friend Christine McSween to help me understand. And that’s revisionist. Actually, Christine engaged with me in a Facebook group around this topic and we agreed to turn it into an educational interview for our group and the world.

Christine was drawn to the spiritual and mindfulness aspects of yoga in the beginning, but with further study she learned how amazing the physical body is along with a realization of the need for more education. With increased fervor, in 2015, she began pursuing a kinesiology degree at the University of Calgary with a focus in biomechanics. She teaches yin yoga, gentle yoga and Restorative Exercise.

Here is our conversation.

MM: I have a hazy understanding of a moment arm, but could not verbalize it well enough to get off the island. Can you give me the words?

CM: Can you let me know your definition first? I want to see what you’re working with!

MM: I can’t! I don’t have my own words. My understanding is hazier than I thought. Sigh.

CM: I want to work through this a bit. Do you have a clearer understanding of a “moment” than the “moment arm”?

MM: Sadly, no. I clearly need a biomechanics lesson.

CM: Ok, I know where to start then!

CM: I’m going to draw a picture.

CM: As you can see in the picture, we have isolated the bicep as the force that will lift the forearm (of course we know this is super simplified).

The force in the bicep creates a moment – or rotation about the elbow joint (or axis of rotation). Because the bicep is only 5 cm down the forearm, it needs to create a LOT of force to lift the forearm. This is because the mass of the forearm is also creating a moment about the elbow joint due to gravity.

MM: (interrupting): Could you say a moment is any rotation about a joint? Does that mean there are an infinite number of moments for a given joint?

CM: YES!

CM: Often in biomechanics we talk about “resultant moments” which is the resultant effect of all the moments about a joint. If the resultant moment is not zero (can be negative or positive), then we have a rotation or movement. I will say though, that the center of mass (COM) is a resultant force, since we know gravity impacts the whole arm

MM: First things first. Can you give me an example of a resultant moment being negative or zero with no rotation/movement? And what is the significance of COM being a resultant force.

CM:When a resultant moment is zero, you have an isometric contraction. There are moment’s occurring, but because they cancel out, the resultant moment is zero. This is how we first learn to calculate forces from moments in physics and biomechanics classes. We assume static equilibrium (no movement) to simplify the calculations.

In our case the system of interest is the forearm. If the forearm rotates towards the upper arm (counterclockwise), this is a positive moment. If the forearm rotates clockwise (extending the elbow), this is a negative moment. Of course, if we flipped our picture around, it would be the opposite.

We use a resultant force for the COM because otherwise we would have to calculate every cell’s mass and every cell’s moment arm, which would have us calculating for days, or weeks, or years. Not ideal! Instead, we can actually measure the weight of the whole forearm, and measure one moment arm to the COM of the forearm. Yay! Only one calculation.

MM: Let’s move on to moment arms.

CM: Now a moment arm is the perpendicular distance from the line of force application to the axis of rotation. Or…the moment arm is the distance from the elbow joint, to the attachment of the bicep, as it relates to the angle of the bicep.

MM: I prefer the latter. And would another moment arm be the distance from the elbow to the hand to account for the mass of the forearm?

CM: No, usually the moment arm is to the center of mass. So probably somewhere in the middle of the forearm. If the hand is holding a weight, then there is another moment arm to the hand.

MM: Let me get this straight. Using the picture above, one moment arm is from the elbow joint to where the bicep attaches on the forearm. Another moment arm is from the elbow joint to the center of mass of the forearm, which is likely near the center of the forearm – but this is only if nothing is being held in hand, I assume. Yet another moment arm would be from the elbow joint to a dumbbell, if one were being held. Eh?

CM:You bet! Just remember the moment arm is in relation to the angle of the applied force. If the forearm is at 90 degrees (like in our picture), then the moment arm would be length from the elbow to the dumbbell. However; this will not be the case if the forearm is at an angle. The applied force is no longer perpendicular.

CM: When there is no rock, there is a very tiny angle between the elastic and the stick, which leads to a very tiny moment arm. So more force is needed for rotation. When there is a rock, the angle is much larger, leading to a larger moment arm, so less force is needed for the same amount of rotation.

MM: We are looking at the angle between the “femur” and the “patella,” yes?

CM: No, the patella and the tibia. The femur isn’t within our “system of interest” in this case.

MM: Dammit.

MM: Ok, so we have the force of the muscle and an external force like gravity or a weight creating individual moment arms. Are these opposing forces? Are there others?

CM:They aren’t quite opposing forces, as they are opposing moments. The bicep is creating a positive moment, while the COM, and a weight in the hand would be producing negative moments. This concept might be more simple if you think about a balanced teeter totter. On either side of the fulcrum you have equal forces in the same direction. BUT the moment arms are opposing, creating opposite moments. Does that make sense? Because our bodies are so wonderfully complex, you could add as many forces as you like, or make it is complicated as you like. And this is why resultant moments are used so frequently. When you add everything together, all the moments and forces, what will happen?

MM: I’m hoping that is a rhetorical question! I suppose it would determine if and how movement happens around a given joint or all joints….

MM: I’m guessing that moment arms are more straightforward, when we are talking about hinge joints like elbows, right? But more complex if we are talking about, say, the scapula?

CM: It would still be the same process, but yes, more difficult to quantify merely because the moment arm would be so small, because of the angles involved.

MM: Wouldn’t there be multiple forces applied to a scapula since it has multiple muscular attachments, moves in multiple planes, and is involved in multiple joints? What is the relationship ship between multiple moment arms and movement in a joint as complex as the shoulder complex?

CM:Simply, this complex structure allows for almost infinite variability in movement. Which logically, makes sense. If our shoulders are “less stable” to allow for more movement, it would make sense to have a variety of options in order to make those movements happen.

MM: So what? Who cares? How is this useful information for a movement practitioner?

CM:Understanding moments and forces allows us to be creative with our cueing and provides a greater understanding of alignment. Plus, we can see how anatomy impacts our biomechanics. In my 21 Day Biomechanics Challenge , I will be using my friend and I as an example.

MM: I thought it might be illuminating to bring in a yoga pose for you to identify forces and moment arms. I give a shout out to this Yoga Stick Figure from Justine Aldersey-Williams. I’ve been using her clever illustrations in my teaching materials for several years now. You can download over 200 images from her Etsy store for just $5.

Image: Justine Aldersey-Williams

MM: Let’s take one of these arrows that you’ve drawn on the figure and tell me what’s going on.

CM: Consider this a static triangle, so the sum of all the moments equals zero. And we want to know the effect of placing the hand on the ground/leg or block vs. having it hover. To remain static, how would the resultant forces of the back leg and obliques change? If the hand is hovering, the resultant forces in the leg and obliques would have to increase to prevent the torso from rotating clockwise towards the ground. When the hand is pressing against something, it provides an opposing force that will rotate the torso counterclockwise, and the resultant forces in the back leg will be smaller. You can try this yourself by practicing both situations. What takes more effort?

MM: That’s fantastic!

MM: I have one final question. If we are biotensegrity systems (and not lever systems) with fascia deeply and exquisitely investing our connective tissues, how should this interconnectivity influence how we think about moments and moment arms in movement?

CM:This is a question I have been struggling with for a couple years now, trying to put my thoughts to words. I must emphasize that my answer to this question will probably evolve over time as I learn more.

Although yes, we are not built like traditional buildings, and are amazingly adaptable tension systems made for mobility, this does not negate the importance of traditional biomechanics. Neither system is wrong, they are just different models, or filters by which we can understand the physical world.

And I think you can combine these models. If you take a tensegrity structure, and expose it to an external force, a moment may still be created. That entire structure might rotate. Or deform. Or translate. There are a number of options.

I think people can assume that this model will destroy the old, but there is not much evidence for that at this time. Biomechanics researchers understand that the body is not a bunch of simple levers. Load is distributed throughout the structure – like tensegrity! But this doesn’t mean that classical biomechanics has no place. Especially when we are starting to learn these concepts. As you study further into biomechanics, you must take into account our biology – how biological tissues respond to forces.

Muscles DO produce force to cause rotation. So we need both models to understand what’s happening in the body as we move. Levers exist, and yet we are this system of tension and compression. As we lift the forearm, not only the muscles such as the bicep, and brachialis lift the forearm, but the triceps create tension and can also contribute eccentric forces, while muscles in the shoulder and chest create stability.

The biotensegrity model informs classical biomechanics, and helps us question our assumptions, but it does not negate the model. If I may quote Jules Mitchell, “Such theories provide a foundation for forward and radical thinking, but are prone to become “buzzwords” which dilute scientific understanding among the mainstream.”

So, why does this stuff matter? The article that started this conversation shows a fantastic combination of questioning classical biomechanics, and informing it with the biotensegrity model. But the basic elements of moments and forces don’t disappear. We still need to understand these concepts to help us move forward.

“The key point is that stability is context specific, depending on the system and the task being performed.” I think this statement could be applicable to many other areas of the body.

And there you have it. A big thank you to Christine for her generous time in taking complex biomechanical concepts and explaining them in the concept of yoga.

About me

I teach Yoga, Restorative Movement, and best practices to strengthen, stretch and mobilize ankles and feet.
I learn by writing. My blog is where I write about what I know and what I am learning about movement.
I am not an expert on feet or alignment or stretching or any of the subjects that I write about, but I hope to bring to bear my expertise as a former research librarian and current student of many body movement fields, to take potentially complicated information, distill it, and communicate it to you so that you can take charge of the health of your feet and all that they carry.